/*
 * @(#)k_sin.c	1.12 06/10/10
 *
 * Copyright  1990-2008 Sun Microsystems, Inc. All Rights Reserved.  
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER  
 *   
 * This program is free software; you can redistribute it and/or  
 * modify it under the terms of the GNU General Public License version  
 * 2 only, as published by the Free Software Foundation.   
 *   
 * This program is distributed in the hope that it will be useful, but  
 * WITHOUT ANY WARRANTY; without even the implied warranty of  
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU  
 * General Public License version 2 for more details (a copy is  
 * included at /legal/license.txt).   
 *   
 * You should have received a copy of the GNU General Public License  
 * version 2 along with this work; if not, write to the Free Software  
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  
 * 02110-1301 USA   
 *   
 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa  
 * Clara, CA 95054 or visit www.sun.com if you need additional  
 * information or have any questions. 
 *
 */

/* __kernel_sin( x, y, iy)
 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
 * Input y is the tail of x.
 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
 *
 * Algorithm
 *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
 *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
 *	3. sin(x) is approximated by a polynomial of degree 13 on
 *	   [0,pi/4]
 *		  	         3            13
 *	   	sin(x) ~ x + S1*x + ... + S6*x
 *	   where
 *
 * 	|sin(x)         2     4     6     8     10     12  |     -58
 * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
 * 	|  x 					           |
 *
 *	4. sin(x+y) = sin(x) + sin'(x')*y
 *		    ~ sin(x) + (1-x*x/2)*y
 *	   For better accuracy, let
 *		     3      2      2      2      2
 *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
 *	   then                   3    2
 *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
 */

#include "fdlibm.h"

#ifdef __STDC__
static const double
#else
static double
#endif
half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */

#ifdef __STDC__
	double __kernel_sin(double x, double y, int iy)
#else
	double __kernel_sin(x, y, iy)
	double x,y; int iy;		/* iy=0 if y is zero */
#endif
{
	double z,r,v,temp;
	int ix;
	ix = __HI(x)&0x7fffffff;	/* high word of x */
	if(ix<0x3e400000)			/* |x| < 2**-27 */
	   {if((int)x==0) return x;}		/* generate inexact */
	/* z	=  x*x; */
	z = CVMdoubleMul(x, x);
	/* v	=  z*x; */
	v = CVMdoubleMul(z, x);
	/* r	=  S2+z*(S3+z*(S4+z*(S5+z*S6))); */
	temp = CVMdoubleMul(S6, z);
	temp = CVMdoubleAdd(temp, S5);
	temp = CVMdoubleMul(temp, z);
	temp = CVMdoubleAdd(temp, S4);
	temp = CVMdoubleMul(temp, z);
	temp = CVMdoubleAdd(temp, S3);
	temp = CVMdoubleMul(temp, z);
	r = CVMdoubleAdd(temp, S2);

	if(iy==0) {
	    /* return x+v*(S1+z*r); */
	    temp = CVMdoubleMul(r, z);
	    temp = CVMdoubleAdd(temp, S1);
	    temp = CVMdoubleMul(temp, v);
	    temp = CVMdoubleAdd(temp, x);
	    return temp;
	} else {
	    /* return x-((z*(half*y-v*r)-y)-v*S1); */
	    double temp2;
	    temp2 = CVMdoubleMul(r, v);
	    temp = CVMdoubleMul(y, half);
	    temp = CVMdoubleSub(temp, temp2);
	    temp = CVMdoubleMul(temp, z);
	    temp = CVMdoubleSub(temp, y);
	    temp2 = CVMdoubleMul(S1, v);
	    temp = CVMdoubleSub(temp, temp2);
	    temp = CVMdoubleSub(x, temp);
	    return temp;
	}
}
